Recent automobiles and vehicles have been built with on-board safety systems which include radar systems for detecting a location or relative velocity of an object or target with respect to the vehicle so that a driver or a collision-avoidance device can react accordingly. A radar system includes a transmitter for sending out a source signal and a receiver for receiving an echo signal or reflection of the source signal from the target. The received signal is sampled at a selected sampling frequency and the sampled data points of the received signal are entered into a Fast Fourier Transform (FFT) in order to determine a frequency of the returning signal. A range or relative velocity of the target with respect to the vehicle can be determined from this frequency.
Due to the discrete nature of the FFT, the frequency spectrum resulting from the FFT displays high sidelobes and frequency smearing whenever the frequency of the echo signal is not the same as a central frequency of a frequency bin. These aberrations reduce the ability of the radar system to determine the frequency of the echo signal and thus to determine a location or relative velocity of the object. While increasing the length of the FFT increases the frequency resolution, such methods require additional hardware and longer computation times. Accordingly, it is desirable to provide a method for quickly and efficiently determining the frequency of the echo signal within a selected resolution.